The database currently contains all extension fields of $\Q_p$ of degree $n$ up to isomorphism for primes $p<150$ and $1\leq n \leq 11$.

## Browse local number fields

The table gives for each $p$ and $n$ shown, the number of degree $n$ extension fields of $\Q_p$ up to isomorphism.

$p$ \ $n$ | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
---|---|---|---|---|---|---|---|---|---|---|

2 | 7 | 2 | 59 | 2 | 47 | 2 | 1823 | 3 | 158 | 2 |

3 | 3 | 10 | 5 | 2 | 75 | 2 | 8 | 795 | 6 | 2 |

5 | 3 | 2 | 7 | 26 | 7 | 2 | 11 | 3 | 258 | 2 |

7 | 3 | 4 | 5 | 2 | 12 | 50 | 8 | 7 | 6 | 2 |

11 | 3 | 2 | 5 | 6 | 7 | 2 | 8 | 3 | 18 | 122 |

13 | 3 | 4 | 7 | 2 | 12 | 2 | 11 | 7 | 6 | 2 |

17 | 3 | 2 | 7 | 2 | 7 | 2 | 15 | 3 | 6 | 2 |

19 | 3 | 4 | 5 | 2 | 12 | 2 | 8 | 13 | 8 | 2 |

23 | 3 | 2 | 5 | 2 | 7 | 2 | 8 | 3 | 6 | 12 |